Evolution of f_NLto the adiabatic limit

Abstract

We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay-the "adiabatic limit". We use numerical methods to explore the sensitivity of the local-shape bispectrum to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of f NL to be large. Other examples can be constructed using a waterfall field to terminate inflation while f NL is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak f NL .

Influence of reheating on the trispectrum and its scale dependence

“…As we have found in our previous work [27] for the case of f NL (see also [26]), we find the trispectrum will in general be sensitive to the decay rates during reheating, although in some cases in which both fields oscillate after inflation, the sensitivity to the decay rates can be very small provided that the decay rates are equal. In general the evolution during reheating is large enough that a comparison of observable values between end of inflation and the final time would lead to the wrong conclusions, since the change in observables may be larger than the expected error bars of the observables.…”

“…Both fields can now decay to the effective radiation fluid and be directly involved in reheating. The model considered is the effective two-field End of Inflation, λ = 0.05 description of axion N-flation, where the potential given by [26] …”

“…To generate a large nonGaussianity, we must have ϕ close to the "hilltop" at horizon-crossing [26]. In this configuration, the second field χ, drives inflation.…”

“…As emphasised in [26,27], ζ continues to evolve after horizon-crossing in the presence of isocurvature modes, and therefore so does its statistics. Thus it is important to take into account any superhorizon evolution up to the point where all isocurvature modes are exhausted, in order to evaluate the true model predictions for the statistics of ζ to compare against observations.…”

Inflation and String Theory

“…Moreover, the five entropic perturbations decay exponentially after exiting the horizon [255]: i.e. an 'adiabatic limit' [683] is reached. This is important, for if one or more entropic perturbations were to persist until the time of reheating, predicting the scalar power spectrum would become extremely difficult [683].…”